Re: Split or Irreducible

In article <1114115251.075767.199410@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<jamesdickerson00@xxxxxxxxxxx> wrote:
>Let E be a subset of the Complex numbers and assume r=e^(2*pi*i)/p be
>in E where p is a prime number. Let a be arbitrary in E. Show that
>the polynomial f(x)=(x^p)-a is irreducible or splits in E[x].
>
>I know that r must be the key to the problem but I don't know how to
>use it.

E is a "subset" of C? Just a subset? We're not assuming closed under
products, sums, anything?

I assume you mean "subfield"... Assuming that:

If u is a root for f(x), how much is f(ru)?


--
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"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
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Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

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